Question

If the product of the matrix B = $\begin{bmatrix} 2 & 6 & 4 \ 1 & 0 & 1 \

• 1 & 1 & - 1 \end{bmatrix}$with a matrix A has inverse C =$\begin{bmatrix}
• 1 & 0 & 1 \ 1 & 1 & 3 \ 2 & 0 & 2 \end{bmatrix}$, then A^–1 equals-

• A. $\begin{bmatrix}
  • 3 & - 5 & 5 \ 0 & 9 & 14 \ 2 & 2 & 6 \end{bmatrix}$
• B. $\begin{bmatrix}
  • 3 & 5 & 5 \ 0 & 0 & 9 \ 2 & 14 & 16 \end{bmatrix}$
• C. $\begin{bmatrix}
  • 3 & - 5 & - 5 \ 0 & 0 & 2 \ 2 & 14 & 6 \end{bmatrix}$
• D. $\begin{bmatrix}
  • 3 & - 3 & - 5 \ 0 & 9 & 2 \ 2 & 14 & 6 \end{bmatrix}$

Answer 1

Answer: (C)

$\begin{bmatrix}

• 3 & - 5 & - 5 \ 0 & 0 & 2 \ 2 & 14 & 6 \end{bmatrix}$

Answer 2

We have (BA)^–1 = C Ž A^–1 B^–1 = C Ž A^–1 = CB

\ A^–1 = $\begin{bmatrix}

• 1 & 0 & 1 \ 1 & 1 & 3 \ 2 & 0 & 2 \end{bmatrix}$$\begin{bmatrix} 2 & 6 & 4 \ 1 & 0 & 1 \
• 1 & 1 & - 1 \end{bmatrix}$=$\begin{bmatrix}
• 3 & - 5 & - 5 \ 0 & 9 & 2 \ 2 & 14 & 6 \end{bmatrix}$